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5.3 Definite Integrals and Antiderivatives

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Page 285 gives rules for working with integrals, the most important of which are: 2. If the upper and lower limits are equal, then the integral is zero. 1. Reversing the limits changes the sign. 3. Constant multiples can be moved outside.

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1. If the upper and lower limits are equal, then the integral is zero. 2. Reversing the limits changes the sign. 3. Constant multiples can be moved outside. 4. Integrals can be added and subtracted.

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4. Integrals can be added and subtracted. 5. Intervals can be added (or subtracted.)

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2 9 -2

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1 -6 1

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The average value of a function is the value that would give the same area if the function was a constant:

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Exploration Activity

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How long is the average chord of a circle with radius r?

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The mean value theorem for definite integrals says that for a continuous function, at some point on the interval the actual value will equal to the average value. Mean Value Theorem (for definite integrals) If f is continuous on then at some point c in,

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